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				<a href="/category/image/2021-02-18-cat-mapping.html" class="noline">
				
                   
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    <span class="date">February 18, 2021</span>
    <a href="/category/image/2021-02-18-cat-mapping.html">
        <h1>Arnold变换</h1>
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    <p class="post-content">在数字水印方案中，单纯地用各种信息隐藏加密算法对秘密信息进行加密是不安全的，因为攻击者只要破解了加密算法，就可能直接提取出秘密信息。针对这一点，我们提出在秘密信息隐藏之前，先对其进行置乱处理，使其失去本身原有的面目，再隐藏到载体中，以确保信息的安全性。以Fibonacci变换和Arnold变换的实验结果阐述了数字图像置乱方法在数字水印中的作用，并提了出一种利用Arnold反变换恢复图像的方法。 一、数字图像置乱的目的 到目前为止，比较成熟的信息隐藏算法基本上都是以图像作为载体的。图像置乱，顾名思义，就是把图像打乱，隐藏原始图像的真实内容。数字图像置乱和信息文件加密思想类似，它主要是通过对数字图像的像素位置做变换来“扰乱”图像，使其变得面目全非、杂乱无章，从而隐藏图像所要表达的真实信息。图像置乱可以达到两个目的： 1、加密处理 图像置乱变换是一种基于内容的图像加密方法，与不知道密钥对已加密信息进行解密一样，倘若不知道图像置乱所采用的算法，同样难以恢复原始图像的信息。 2、增强图像伪装的鲁棒性 置乱技术作为信息隐藏的预处理手段，可以大大增强图像信息伪装的鲁棒性。主要体现在3个方面： ①图像置乱以后，将得到一幅杂乱无序的图像，没有内容，没有纹理，也没有形状，从中无法读取出有意义的信息。 我们将这样一幅“三无”图像嵌入到另一幅普通图像里时就不易引起这幅图像在内容、纹理、形状上的太大改变，甚至觉察不出发生了改变，这样人眼就不易识别，从而逃出了第三方的视线，可以更好地保证水印信息的隐蔽性。 ②由于秘密图像是置乱以后的图像，第三方难以对它的内容、纹理、形状等进行统计分析，这样即便他们截获到了秘密图像，也对此无能为力。如果第三方企图对秘密图像进行反置乱运算，这也是非常困难的，因为图像置乱的方法很多，每种方法又可以使用不同的置乱算法，设置不同的参数，加密方可以根据自己的想法得到很多不同的结果，这给企图进行反置乱的第三方带来了很大的困难，需要耗费巨大的计算量来穷举测试各种可能性。 ③如果第三方进行反置乱运算不成，也可能会在隐蔽的载体上进行恶意修改，用置乱的方法也可以达到抵抗这些攻击的目的。因为合法接收者对秘密图像进行反置乱的时候，会使第三方在图像上所涂画的信息分散到画面的各个位置，形成点状的随机噪声，对视觉影响的程度不是很大。 图1是在置乱图像上进行涂改和剪裁两种恶意修改以后，恢复出的秘密图像。可以看到，秘密图像的内容依然可见。为了使提取的图像信息更为清晰，还可以对破坏严重的图像进行中值滤波等方面的处理，以去除随机噪声。 当然，不应该忽视的是图像置乱在一定程度上增加了加密计算的复杂度和计算量，但是与非法攻击者可能花费的更大的计算量相比，图像置乱仍是一种值得付出代价的、相对安全的手段。正是因为如此，图像置乱技术在数字水印技术中具有非常重要的作用和意义。 二、数字图像置乱的方法 数字图像的置乱可以在位置空间、色彩空间、频率空间上进行。随着计算机技术和数字图像处理技术的发展，很多文献对图像置乱提出了不同的置乱算法，大体上可以分为线性变换、几何变换和仿射变换。目前研究较多的置乱技术包括Fibonacci变换、Arnold变换、Hilbert曲线变换、E-曲线变换、Gray变换、仿射变换、幻方、正交拉丁方变换等方法。无论哪一种置乱技术都是可逆的，或者是具有周期性的，即多次迭代或者做反变换均能恢复原图像。...</p>
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				<a href="/category/deeplearning/2021-02-05-reduced-neural-network-size-six-times-without-post-training.html" class="noline">
				
                   
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    <span class="date">February 05, 2021</span>
    <a href="/category/deeplearning/2021-02-05-reduced-neural-network-size-six-times-without-post-training.html">
        <h1>模型压缩6倍，无需重训练</h1>
    </a>
    <p class="post-content">RUDN 大学的数学家团队找到一种新方法，该方法能够让神经网络的大小减小到六分之一，且无需花费更多的资源重新训练。 神经网络压缩是指在对神经网络性能影响不大的情况下，通过有关方法来减少网络的参数和存储空间，大体上可以分为近似，量化和剪枝三类方法。 近日，来自俄罗斯人民友谊大学（RUDN）的数学家团队找到一种方法，可以将训练后的神经网络的大小减小六倍，而无需花费更多的资源来对其进行重新训练。该方法基于找到初始系统及其简化版本中神经连接权重之间的相关性。这项研究的结果发表在《Optical Memory and Neural Networks》期刊上。 生命体中人工神经网络和神经元的结构是基于相同的原理。网络中的节点是相互连接的；其中一些接收信号，一些通过激活或抑制链中的下一个元素来发送信号。任何信号（例如图像或声音）的处理都需要很多网络元素及其之间的连接。但是，计算机模型只有有限的模型容量和存储空间。为了处理大量数据，这一领域的研究者必须发明各种方法来降低对模型能力的需求，包括所谓的量化。这有助于减少资源消耗，但需要对系统进行重新训练。RUDN 大学的一些数学家发现后者可以避免。 RUDN 大学 Nikolskii 数学研究所助理教授 Iakov...</p>
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				<a href="/category/deeplearning/2019-06-03-quickly-understand-svm.html" class="noline">
				
                   
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    <span class="date">June 03, 2019</span>
    <a href="/category/deeplearning/2019-06-03-quickly-understand-svm.html">
        <h1>快速看懂支持向量机</h1>
    </a>
    <p class="post-content">1 前言 支持向量机（support vector machines，SVM）是我最早接触的有监督分类算法之一。早在 MIT 修统计学的时候，我用它做过一个旧金山湾区上班族通勤模式的分类研究，但当时只是很粗浅的认识。后来由于工作的关系又非常系统的学习了一下，这其中包括认真学习了斯坦福 Andrew Ng（吴恩达）的机器学习课（吴讲的真的非常好，深入浅出），参阅了大量的关于 SVM 的理论和实际应用的文献。 对于有监督分类算法的表现，业界常用大概 10 种不同的指标来评判，包括 Accuracy，LIFT，F-Score，ROC，Precision...</p>
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				<a href="/category/mathematics/2015-09-10-matrix-operation.html" class="noline">
				
                   
                    <img src="http://www.upare.net/tools/images/quote?savepath=quoteimg/brainscc&url=http://www.ruanyifeng.com/blogimg/asset/2015/bg2015090114.jpg">
                    
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    <span class="date">September 10, 2015</span>
    <a href="/category/mathematics/2015-09-10-matrix-operation.html">
        <h1>理解矩阵运算</h1>
    </a>
    <p class="post-content">刚学的时候，还蛮简单的，矩阵加法就是相同位置的数字加一下。 矩阵减法也类似。 矩阵乘以一个常数，就是所有位置都乘以这个数。 但是，等到矩阵乘以矩阵的时候，一切就不一样了。 这个结果是怎么算出来的？ 教科书告诉你，计算规则是，第一个矩阵第一行的每个数字（2和1），各自乘以第二个矩阵第一列对应位置的数字（1和1），然后将乘积相加（ 2 x 1 + 1 x 1），得到结果矩阵左上角的那个值3。 也就是说，结果矩阵第m行与第n列交叉位置的那个值，等于第一个矩阵第m行与第二个矩阵第n列，对应位置的每个值的乘积之和。 怎么会有这么奇怪的规则？...</p>
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